A multipartite Ramsey number for odd cycles

2012 ◽  
Vol 71 (3) ◽  
pp. 293-316 ◽  
Author(s):  
Fabrıcio Siqueira Benevides
Keyword(s):  
Ramsey Number ◽  
Odd Cycles

scholarly journals The 3-colored Ramsey number of odd cycles

2005 ◽  
Vol 19 ◽  
pp. 397-402 ◽  
Author(s):  
Yoshiharu Kohayakawa ◽  
Miklós Simonovits ◽  
Jozef Skokan
Keyword(s):  
Ramsey Number ◽  
Odd Cycles

scholarly journals New upper bound for multicolor Ramsey number of odd cycles

2019 ◽  
Vol 342 (1) ◽  
pp. 217-220 ◽  
Author(s):  
Qizhong Lin ◽  
Weiji Chen
Keyword(s):  
Upper Bound ◽  
Ramsey Number ◽  
Multicolor Ramsey Number ◽  
Odd Cycles

scholarly journals A Note on On-Line Ramsey Numbers for Some Paths

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 735
Author(s):  
Tomasz Dzido ◽  
Renata Zakrzewska
Keyword(s):  
Ramsey Number ◽  
Ramsey Numbers ◽  
Minimum Number ◽  
On Line ◽  
Infinite Set ◽  
Do So

We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent vertices with an edge, and the Painter colors the edge red or blue. An on-line Ramsey number r˜(G,H) is the minimum number of rounds it takes the Builder to force the Painter to create a red copy of graph G or a blue copy of graph H, assuming that both the Builder and Painter play perfectly. The Painter’s goal is to resist to do so for as long as possible. In this paper, we consider the case where G is a path P4 and H is a path P10 or P11.

scholarly journals New values for the bipartite Ramsey number of the four-cycle versus stars

2021 ◽  
Vol 344 (5) ◽  
pp. 112320
Author(s):  
Imre Hatala ◽  
Tamás Héger ◽  
Sam Mattheus
Keyword(s):  
Ramsey Number

scholarly journals On the size Ramsey number of all cycles versus a path

2021 ◽  
Vol 344 (5) ◽  
pp. 112322
Author(s):  
Deepak Bal ◽  
Ely Schudrich
Keyword(s):  
Ramsey Number

Solar-cycle phenomena in cosmic-ray intensity: Differences between even and odd cycles

1988 ◽  
Vol 42 (3) ◽  
pp. 233-244 ◽  
Author(s):  
H. Mavromichalaki ◽  
E. Marmatsouri ◽  
A. Vassilaki
Keyword(s):  
Solar Cycle ◽  
Cosmic Ray ◽  
Cosmic Ray Intensity ◽  
Odd Cycles

scholarly journals Ramsey Numbers for Theta Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
M. M. M. Jaradat ◽  
M. S. A. Bataineh ◽  
S. M. E. Radaideh
Keyword(s):  
Complete Graph ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Subgraph Isomorphic

The graph Ramsey number is the smallest integer with the property that any complete graph of at least vertices whose edges are colored with two colors (say, red and blue) contains either a subgraph isomorphic to all of whose edges are red or a subgraph isomorphic to all of whose edges are blue. In this paper, we consider the Ramsey numbers for theta graphs. We determine , for . More specifically, we establish that for . Furthermore, we determine for . In fact, we establish that if is even, if is odd.

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